%0 Journal Article %1 fang_homological_2008 %A Fang, Bohan %D 2008 %J 0804.0646 %K Mirror Symmetry %T Homological mirror symmetry is T-duality for \$\textbackslashmathbb Pˆn\$ %U http://arxiv.org/abs/0804.0646 %X In this paper, we apply the idea of T-duality to projective spaces. From a connection of a line bundle on \$\textbackslashmathbb Pˆn\$, a Lagrangian in the mirror Landau-Ginzburg model is constructed. Under this correspondence, the full strong exceptional collection \$\textbackslashmathcal O\_\textbackslashmathbb Pˆn(-n-1),...,\textbackslashmathcal O\_\textbackslashmathbb Pˆn(-1)\$ is mapped to standard Lagrangians in the sense of Nadler-Zaslow. Passing to constructible sheaves, we explicitly compute the quiver structure of these Lagrangians, and find that they match the quiver structure of this exceptional collection of \$\textbackslashmathbb Pˆn\$. In this way, T-duality provides quasi-equivalence of the Fukaya category containing these Lagrangians and the category of coherent sheaves on \$\textbackslashmathbb Pˆn\$, which is a kind of homological mirror symmetry.

@article{fang_homological_2008, abstract = {In this paper, we apply the idea of T-duality to projective spaces. From a connection of a line bundle on \${\textbackslash}mathbb P{\textasciicircum}n\$, a Lagrangian in the mirror {Landau-Ginzburg} model is constructed. Under this correspondence, the full strong exceptional collection \${\textbackslash}mathcal O\_{{\textbackslash}mathbb P{\textasciicircum}n}(-n-1),...,{\textbackslash}mathcal O\_{{\textbackslash}mathbb P{\textasciicircum}n}(-1)\$ is mapped to standard Lagrangians in the sense of {Nadler-Zaslow.} Passing to constructible sheaves, we explicitly compute the quiver structure of these Lagrangians, and find that they match the quiver structure of this exceptional collection of \${\textbackslash}mathbb P{\textasciicircum}n\$. In this way, T-duality provides quasi-equivalence of the Fukaya category containing these Lagrangians and the category of coherent sheaves on \${\textbackslash}mathbb P{\textasciicircum}n\$, which is a kind of homological mirror symmetry.}, added-at = {2009-05-11T21:36:02.000+0200}, author = {Fang, Bohan}, biburl = {https://www.bibsonomy.org/bibtex/23ef8f00d4be83cbb2150d5f2bb26ec25/tbraden}, interhash = {d250cabb32462488409ca18fdbd52d1f}, intrahash = {3ef8f00d4be83cbb2150d5f2bb26ec25}, journal = {0804.0646}, keywords = {Mirror Symmetry}, month = {April}, timestamp = {2009-05-11T21:36:03.000+0200}, title = {Homological mirror symmetry is T-duality for \${\textbackslash}mathbb P{\textasciicircum}n\$}, url = {http://arxiv.org/abs/0804.0646}, year = 2008 }